I will admit, I find the way statistics are gathered to be confusing. Of all the maths, that one is the hardest for me to get my brain around (and I was always good at math in school and college). So I don't really know what is legit, but much of the time, it sounds sketchy to me simply because of what you noted - how do we know people tested accurately? How much verification of their type is there?
Like many here, I did not test my type initially, nor for many years, and I still often do not test my type (I test INTP much of the time). However, I did not identify with the type I tested, so instead of being mistyped, I simply did not settle on anything. It took more thorough investigation on my part to see I was INFP (because Feeling is so poorly represented on most tests).
I think sometimes those MBTI certified coaches make matters worse too; I've heard they sort of coax people into the type they tested as, and they rely on a lot of behavioral stereotypes. Their knowledge of the Jungian theory and cognitive functions may be poor. So even if they are educating people a bit to help them identify their type, they may still be leading them down the wrong path.